Improved Cox Hazard Model for Loans and Advances Impairment

Abstract

In the report by CBK in March 2014, Non-Performing Loans (NPLs) had increased by 34.4% to KES 77.3 billion in June 2013 raising the percentage of the gross NPLs from 4.5% to 5.3% over the 2012/2013 period. The gross in ation characterised by an increase in prices of goods and services had also increased attributed to bad economic times. The task of this thesis is to design an improved cox proportional hazard (ph) model to analyse the loans default by customers and thereby reduce the NPLs in order to maximize the net returns on loans. The objectives of the project are to determine the survival time of loans, assess if the survival time di ers by the loan category, study the in uence of predictors on survival of a loan and determine to what extent a cox ph model can aid in prediction of the loans default prediction by improving it. Various residual plots are also tted to test for the goodness-of- t, to identify possible outliers and in uential ob- servations in the models and check if the assumptions of the model hold. Such residuals are namely Schoenfeld, Martingale which is an improvement to the cox snell residuals, deviance, and score residuals and we applied those methods on loans data.The aim is to model the loan portfolio for the sampled bank with empirical data on customer credit information and compare the cox ph model versus the improved cox ph model to demon- strate how the cox ph model can be adjusted to t the various management needs. The analyses has been implemented using the Excel and the R-Graphical User Interface soft- ware. The results show that account balance and loan classi cation are highly signi cant in the improved cox ph model than credit amount and value saving stock in determining the de- fault rates of loans. The average survival time for a loan is 16 months for the improved cox proportional model. The improved cox proportional model has an AIC value of 3325.881 and thus a better t to the cox proportional model with an AIC value of 3343.359. Keywords: Cox proportional hazard model, improved cox proportional hazard model, survival time, residuals.